= = - = - 3. (60 points) Study the dynamical behavior of the Lorenz system: · o(y – x), ☺ px — Y – XZ, ż XY – Bz. where

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3 60 Points Study The Dynamical Behavior Of The Lorenz System O Y X Px Y Xz Z Xy Bz Where 1 (160.3 KiB) Viewed 31 times

= = - = - 3. (60 points) Study the dynamical behavior of the Lorenz system: · o(y – x), ☺ px — Y – XZ, ż XY – Bz. where p, o = 10, B = 8/3 are real parameters. (a) (30 points) Perform a numerical study of the system for at least 10 different initial conditions starting close to the origin for at least 1000 time units. Choose p = 28. Visualize your results! Use whatever tools/programming language you like, except assembly language! (b) (30 points) Study the system analytically around all fixed points for fixed values of o 10, B = 8/3! Make use of Extended Center Manifolds! Classify bifurcations as p changes from 0 to 30! - -